Problem 404 Roof Truss - Method of Joints

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Problem 404
Determine the forces in the members of the roof truss shown in Fig. P-404.

Solution 404

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$\Sigma M_D = 0$

$2xR_A = 450x$

$R_A = 225 \, \text{N}$

$\Sigma M_A = 0$

$2xV_D = 450x + (450 \sin 30^\circ)(2x)$

$V_D = 450 \, \text{N}$

$\Sigma F_H = 0$

$H_D = 450 \cos 30^\circ = 389.71 \, \text{N}$

At Joint A
$\Sigma F_V = 0$

$F_{AB} \sin 30^\circ = 225$

$F_{AB} = 450 \, \text{N}$

$\Sigma F_H = 0$

$F_{AC} = F_{AB} \cos 30^\circ = 450 \cos 30^\circ$

$F_{AC} = 389.71 \, \text{N}$

At Joint C
$\Sigma F_V = 0$

$F_{BC} = 450 \, \text{N}$

$\Sigma F_H = 0$

$F_{CD} = 389.71 \, \text{N}$

At Joint B
$\Sigma F_H = 0$

$F_{BD} \cos 30^\circ = 450 \cos 30^\circ + 450 \cos 30^\circ$

$F_{BD} = 900 \, \text{N}$

$\Sigma F_V = 0$

$F_{BD} \sin 30^\circ + 450 \sin 30^\circ = 450 + 450 \sin 30^\circ$

$F_{BD} = 900 \, \text{N}$ Check!

At Joint D
$\Sigma F_V = 0$

$450 = 900 \sin 30^\circ$

$450 = 450$ Check!

$\Sigma F_H = 0$

$900 \cos 30^\circ = 389.71 + 389.71$

$779.42 = 779.42$ Check!

Summary
AB = 450 N compression
AC = 389.71 N tension
BC = 450 N tension
BD = 900 N compression
CD = 389.71 N tension

‹ Problem 403 | Method of Joints up Problem 405 | Method of Joints ›

Submitted by Romel Verterra on January 30, 2013 - 9:14pm

3997 reads

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Engineering Mechanics

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